Robust balancing for rotating machines

The balancing of rotors divides broadly into two categories: balancing in situ and balancing in a balancing machine. In the latter case, the most common practice is to arrange balance corrections on the rotor such that the net excitations of each of the four in-plane rigid-body modes of the free rotor is zero by deploying balance corrections on two independent planes. In a small proportion of cases, the net excitations of the first pair of flexural modes are also zeroed using a third correction plane. This paper proposes that, when rotors are balanced in a balancing machine (not similar to the machine stator), substantially more utility can be gained from the balancing operation by combining a suitably weighted account of the specific balancing requirements of the machine with knowledge of the expected machine characteristics than can be achieved by ignoring this knowledge. A single cost function is established based on a numerical model of the machine. Then, depending on circumstances, either the expected value of this cost function or its worst possible value can be minimized. The methods proposed require that relatively detailed knowledge of the distribution of residual unbalance be obtained experimentally. The paper briefy discusses some practical methods for how such information might be extracted. The de?nition of the cost function as a matrix quadratic form provides potentially valuable information about the necessary number and the optimal location of balance planes on a given rotor, and methods for determining an optimal set of balance planes are outlined.